A sine wave contains how many frequencies?

• A. Only one
• B. Two
• C. Many
• D. Zero

Answer: (A)

A sine wave is a pure tone with a single frequency. It repeats at a constant rate, defined by one frequency, and does not include any harmonic content. In Fourier terms, a complex signal can be broken into frequency components, but a pure sine already consists of just one frequency component, so its spectrum has energy at only that one frequency. In listening terms, you hear one pitch. (As a side note, in the mathematical Fourier view a real sine can be represented as two complex exponentials at positive and negative that frequency, but this doesn’t add new pitches—it’s just another way to describe the same single tone.) Therefore, a sine wave contains only one frequency.